How to Efficiently Handle Complex Values? Implementing Decision Diagrams for Quantum Computing

Abstract

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum functionality. In the classical domain, decision diagrams have been successfully employed as a powerful alternative to straightforward means such as truth tables. This motivated extensive research on whether decision diagrams provide similar potential in the quantum domain-resulting in new types of decision diagrams capable of substantially reducing the complexity of representing quantum states and functionality. From an implementation perspective, many concepts and techniques from the classical domain can be re-used in order to implement decision diagrams packages for the quantum realm. However, new problems-namely how to efficiently handle complex numbersarise. In this work, we propose a solution to overcome these problems. Experimental evaluations confirm that this yields improvements of orders of magnitude in the runtime needed to create and to utilize these decision diagrams. The resulting implementation is publicly available as a quantum DD package at http://iic.jku.at/eda/research/quantum dd.

Considering decoherence errors in the simulation of quantum circuits using decision diagrams

“…In this section, we summarize the core results of our evaluations conducted in order to investigate the effect of considering decoherence errors in the simulation of quantum circuits using decision diagrams. To this end, we took the state-of-the-art decision diagram-based simulator from [32,34] and extended this implementation to additionally support decoherence errors. This led to one version in which error support has been added in a straightforward fashion (i.e., directly applying the concepts described in Section 3.1) and another version in which error support has been added in an advanced fashion (i.e., applying the methods described in Section 4).…”

Tools for Quantum Computing Based on Decision Diagrams

“…Additionally selected quantum algorithms such as Grover's search and Shor's algorithm are directly integrated as classesÐallowing to programatically construct the respective quantum circuits for simulation, compilation, or veriication with parameters controlling, e.g., the number qubits. The QFR itself depends on a package providing the functionality for representing and manipulating quantum states and operations via decision diagrams [50,53]. The DD package has options that are set during compile time to enable more aggressive compiler optimizations and inluence the later execution in simulation and veriication.…”

“…Depending on the required precision, the developer may change this to float (less precision with faster execution) or long double (higher precision but slower execution). If the precision is changed, this should be relected in the TOLERANCE (deined in include/dd/ComplexTable.hpp) which mitigates efects caused by the fundamentally limited precision in the representation of complex numbers [50]. Support for additional łhardcodedž algorithms or ile formats should be integrated into the QFR, so the tools for simulation, veriication, and visualization can access these new features.…”

JKQ

“…Additionally selected quantum algorithms like Grover's search and Shor's algorithm are directly integrated as classes-allowing to programatically construct the respective quantum circuits for simulation, compilation, or verification with parameters controlling, e.g., the number qubits. The QFR itself depends on a package providing the functionality for representing and manipulating quantum states and operations via decision diagrams [21,24]. Example 8.…”

“…Depending on the required precision, the developer may change this to float (less precision with faster execution) or long double (higher precision but slower execution). If the precision is changed, this should be reflected in the TOLERANCE (both are defined in DDcomplex.h) which mitigates effects caused by the fundamentally limited precision in the representation of complex numbers [21]. Support for additional "hardcoded" algorithms or file formats should be integrated into the QFR, so the tools for simulation, mapping, and verification can access these new features.…”